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Hedonic coalition formation games: A new stability notion

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  • Karakaya, Mehmet

Abstract

This paper studies hedonic coalition formation games where each player's preferences rely only upon the members of her coalition. A new stability notion under free exit-free entry membership rights, referred to as strong Nash stability, is introduced which is stronger than both core and Nash stabilities studied earlier in the literature. Strong Nash stability has an analogue in non-cooperative games and it is the strongest stability notion appropriate to the context of hedonic coalition formation games. The weak top-choice property is introduced and shown to be sufficient for the existence of a strongly Nash stable partition. It is also shown that descending separable preferences guarantee the existence of a strongly Nash stable partition. Strong Nash stability under different membership rights is also studied.

Suggested Citation

  • Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
  • Handle: RePEc:eee:matsoc:v:61:y:2011:i:3:p:157-165
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    1. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    2. Conley, John P. & Konishi, Hideo, 2002. "Migration-proof Tiebout equilibrium: existence and asymptotic efficiency," Journal of Public Economics, Elsevier, vol. 86(2), pages 243-262, November.
    3. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
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    5. José Alcalde & Antonio Romero-Medina, 2006. "Coalition Formation and Stability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 365-375, October.
    6. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    7. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
    8. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    9. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
    10. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    11. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
    12. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
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    1. repec:the:publsh:2870 is not listed on IDEAS
    2. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    3. Gallo Fernández, Ohiane & Iñarra García, Elena, 2016. "Rationing Rules and Stable Coalition Structures," IKERLANAK Ikerlanak;2016-100, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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